No, Shazam does’t have a web based service at this stage. Shazam does have a Windows 10 native app for desktop which will be your best solution. This is something that we use at work frequently. However, Shazam doesn’t have a dedicated Windows application.
Additionally, SoundHound has a website at www.midomi.com (incidentally, SoundHound used to be called Midomi) that does this, albeit with less accessory features than the app.